Boundedness and Compactness of products of Toeplitz operators on the Bergman Space

Details Boundedness and Compactness of products of Toeplitz operators on the Bergman Space Boundedness and Compactness of products of Toeplitz operators on the Bergman Space

2007-08-20

arxiv.org/abs/0708.2635v1

Mathematics

Complex Variables

10 pages

Scientific paper

In a celebrated conjecture D.Sarason stated a necessary and sufficient condition on the symbols f, g in the Bergman space, L^2_a(\Delta) of the unit disk, \Delta, for the products T_{f}T_{\bar g} of associated Toeplitz operators to be bounded (respectively compact) on L^2_a(\Delta) . K. Stroethoff and D. Zheng proved that these conditions are necessary. We prove the sufficiency of these conditions, thus solvind Sarason's conjecture.

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